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SphericalCoordinates (Commons Math 3.2 API)
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org.apache.commons.math3.geometry.euclidean.threed</FONT>
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Class SphericalCoordinates</H2>
<PRE>
<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</A>
  <IMG SRC="../../../../../../../resources/inherit.gif" ALT="extended by "><B>org.apache.commons.math3.geometry.euclidean.threed.SphericalCoordinates</B>
</PRE>
<DL>
<DT><B>All Implemented Interfaces:</B> <DD><A HREF="http://download.oracle.com/javase/6/docs/api/java/io/Serializable.html?is-external=true" title="class or interface in java.io">Serializable</A></DD>
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<HR>
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<DT><PRE>public class <B>SphericalCoordinates</B><DT>extends <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A><DT>implements <A HREF="http://download.oracle.com/javase/6/docs/api/java/io/Serializable.html?is-external=true" title="class or interface in java.io">Serializable</A></DL>
</PRE>

<P>
This class provides conversions related to <a
 href="http://mathworld.wolfram.com/SphericalCoordinates.html">spherical coordinates</a>.
 <p>
 The conventions used here are the mathematical ones, i.e. spherical coordinates are
 related to Cartesian coordinates as follows:
 </p>
 <ul>
   <li>x = r cos(&theta;) sin(&Phi;)</li>
   <li>y = r sin(&theta;) sin(&Phi;)</li>
   <li>z = r cos(&Phi;)</li>
 </ul>
 <ul>
   <li>r       = &radic;(x<sup>2</sup>+y<sup>2</sup>+z<sup>2</sup>)</li>
   <li>&theta; = atan2(y, x)</li>
   <li>&Phi;   = acos(z/r)</li>
 </ul>
 <p>
 r is the radius, &theta; is the azimuthal angle in the x-y plane and &Phi; is the polar
 (co-latitude) angle. These conventions are <em>different</em> from the conventions used
 in physics (and in particular in spherical harmonics) where the meanings of &theta; and
 &Phi; are reversed.
 </p>
 <p>
 This class provides conversion of coordinates and also of gradient and Hessian
 between spherical and Cartesian coordinates.
 </p>
<P>

<P>
<DL>
<DT><B>Since:</B></DT>
  <DD>3.2</DD>
<DT><B>Version:</B></DT>
  <DD>$Id: SphericalCoordinates.java 1443364 2013-02-07 09:28:04Z luc $</DD>
<DT><B>See Also:</B><DD><A HREF="../../../../../../../serialized-form.html#org.apache.commons.math3.geometry.euclidean.threed.SphericalCoordinates">Serialized Form</A></DL>
<HR>

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<TD><CODE><B><A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/SphericalCoordinates.html#SphericalCoordinates(double, double, double)">SphericalCoordinates</A></B>(double&nbsp;r,
                     double&nbsp;theta,
                     double&nbsp;phi)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Build a spherical coordinates transformer from spherical coordinates.</TD>
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<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><B><A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/SphericalCoordinates.html#SphericalCoordinates(org.apache.commons.math3.geometry.euclidean.threed.Vector3D)">SphericalCoordinates</A></B>(<A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Vector3D</A>&nbsp;v)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Build a spherical coordinates transformer from Cartesian coordinates.</TD>
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<CODE>&nbsp;<A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Vector3D</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/SphericalCoordinates.html#getCartesian()">getCartesian</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Get the Cartesian coordinates.</TD>
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<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/SphericalCoordinates.html#getPhi()">getPhi</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Get the polar (co-latitude) angle.</TD>
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<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/SphericalCoordinates.html#getR()">getR</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Get the radius.</TD>
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<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/SphericalCoordinates.html#getTheta()">getTheta</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Get the azimuthal angle in x-y plane.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double[]</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/SphericalCoordinates.html#toCartesianGradient(double[])">toCartesianGradient</A></B>(double[]&nbsp;sGradient)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Convert a gradient with respect to spherical coordinates into a gradient
 with respect to Cartesian coordinates.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double[][]</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/SphericalCoordinates.html#toCartesianHessian(double[][], double[])">toCartesianHessian</A></B>(double[][]&nbsp;sHessian,
                   double[]&nbsp;sGradient)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Convert a Hessian with respect to spherical coordinates into a Hessian
 with respect to Cartesian coordinates.</TD>
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<A NAME="SphericalCoordinates(org.apache.commons.math3.geometry.euclidean.threed.Vector3D)"><!-- --></A><H3>
SphericalCoordinates</H3>
<PRE>
public <B>SphericalCoordinates</B>(<A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Vector3D</A>&nbsp;v)</PRE>
<DL>
<DD>Build a spherical coordinates transformer from Cartesian coordinates.
<P>
<DL>
<DT><B>Parameters:</B><DD><CODE>v</CODE> - Cartesian coordinates</DL>
</DL>
<HR>

<A NAME="SphericalCoordinates(double, double, double)"><!-- --></A><H3>
SphericalCoordinates</H3>
<PRE>
public <B>SphericalCoordinates</B>(double&nbsp;r,
                            double&nbsp;theta,
                            double&nbsp;phi)</PRE>
<DL>
<DD>Build a spherical coordinates transformer from spherical coordinates.
<P>
<DL>
<DT><B>Parameters:</B><DD><CODE>r</CODE> - radius<DD><CODE>theta</CODE> - azimuthal angle in x-y plane<DD><CODE>phi</CODE> - polar (co-latitude) angle</DL>
</DL>

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<A NAME="getCartesian()"><!-- --></A><H3>
getCartesian</H3>
<PRE>
public <A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Vector3D</A> <B>getCartesian</B>()</PRE>
<DL>
<DD>Get the Cartesian coordinates.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>Cartesian coordinates</DL>
</DD>
</DL>
<HR>

<A NAME="getR()"><!-- --></A><H3>
getR</H3>
<PRE>
public double <B>getR</B>()</PRE>
<DL>
<DD>Get the radius.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>radius r<DT><B>See Also:</B><DD><A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/SphericalCoordinates.html#getTheta()"><CODE>getTheta()</CODE></A>, 
<A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/SphericalCoordinates.html#getPhi()"><CODE>getPhi()</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="getTheta()"><!-- --></A><H3>
getTheta</H3>
<PRE>
public double <B>getTheta</B>()</PRE>
<DL>
<DD>Get the azimuthal angle in x-y plane.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>azimuthal angle in x-y plane &theta;<DT><B>See Also:</B><DD><A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/SphericalCoordinates.html#getR()"><CODE>getR()</CODE></A>, 
<A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/SphericalCoordinates.html#getPhi()"><CODE>getPhi()</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="getPhi()"><!-- --></A><H3>
getPhi</H3>
<PRE>
public double <B>getPhi</B>()</PRE>
<DL>
<DD>Get the polar (co-latitude) angle.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>polar (co-latitude) angle &Phi;<DT><B>See Also:</B><DD><A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/SphericalCoordinates.html#getR()"><CODE>getR()</CODE></A>, 
<A HREF="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/SphericalCoordinates.html#getTheta()"><CODE>getTheta()</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="toCartesianGradient(double[])"><!-- --></A><H3>
toCartesianGradient</H3>
<PRE>
public double[] <B>toCartesianGradient</B>(double[]&nbsp;sGradient)</PRE>
<DL>
<DD>Convert a gradient with respect to spherical coordinates into a gradient
 with respect to Cartesian coordinates.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>sGradient</CODE> - gradient with respect to spherical coordinates
 {df/dr, df/d&theta;, df/d&Phi;}
<DT><B>Returns:</B><DD>gradient with respect to Cartesian coordinates
 {df/dx, df/dy, df/dz}</DL>
</DD>
</DL>
<HR>

<A NAME="toCartesianHessian(double[][], double[])"><!-- --></A><H3>
toCartesianHessian</H3>
<PRE>
public double[][] <B>toCartesianHessian</B>(double[][]&nbsp;sHessian,
                                     double[]&nbsp;sGradient)</PRE>
<DL>
<DD>Convert a Hessian with respect to spherical coordinates into a Hessian
 with respect to Cartesian coordinates.
 <p>
 As Hessian are always symmetric, we use only the lower left part of the provided
 spherical Hessian, so the upper part may not be initialized. However, we still
 do fill up the complete array we create, with guaranteed symmetry.
 </p>
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>sHessian</CODE> - Hessian with respect to spherical coordinates
 {{d<sup>2</sup>f/dr<sup>2</sup>, d<sup>2</sup>f/drd&theta;, d<sup>2</sup>f/drd&Phi;},
  {d<sup>2</sup>f/drd&theta;, d<sup>2</sup>f/d&theta;<sup>2</sup>, d<sup>2</sup>f/d&theta;d&Phi;},
  {d<sup>2</sup>f/drd&Phi;, d<sup>2</sup>f/d&theta;d&Phi;, d<sup>2</sup>f/d&Phi;<sup>2</sup>}<DD><CODE>sGradient</CODE> - gradient with respect to spherical coordinates
 {df/dr, df/d&theta;, df/d&Phi;}
<DT><B>Returns:</B><DD>Hessian with respect to Cartesian coordinates
 {{d<sup>2</sup>f/dx<sup>2</sup>, d<sup>2</sup>f/dxdy, d<sup>2</sup>f/dxdz},
  {d<sup>2</sup>f/dxdy, d<sup>2</sup>f/dy<sup>2</sup>, d<sup>2</sup>f/dydz},
  {d<sup>2</sup>f/dxdz, d<sup>2</sup>f/dydz, d<sup>2</sup>f/dz<sup>2</sup>}}</DL>
</DD>
</DL>
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